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Two small circular loops, marked (1) and...

Two small circular loops, marked (1) and (2), carrying equal currents are placed with the geometrical axes perpendicular to each other as shown in figure. Find the magnitude and direction of the net magnetic field produced at the point O.

Text Solution

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Magnetic field induction at O due to current loop 1 is
`B_1=(mu_0IR^2)/(2(x^2+R^2)^(3//2))`,
acting towards left.
Magnetic field induction at O due to current loop 2 is
`B_2=(mu_0IR^2)/(2(x^2+R^2)^(3//2))`
acting vertically upwards.
Resultant magnetic field induction at O will be
`B=sqrt(B_1^2+B_2^2)=sqrt2B_1` (`:' B_1=B_2`)
`=sqrt2xx(mu_0IR^2)/(2(x^2+R^2)^(3//2))`
`=(mu_0IR^2)/(sqrt(x^2+R^2)^(3//2))`
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Two small identical circular loops, marked (1) and (2), carrying equal currents are placed with the geometrical axes perpendicular to each other as shown in the fig. Find the fig. Find the magnitude and direction of the net magnetic field at the net magnetic field at the point O.

(a) Using Biot-Savart's law, derive an expression for the magnetic field at the centre of a circular coil of radius R, number of turns N, carrying current. (b) Two small identical circular coils marked 1,2 carry equal currents and are placed with their geometric axes perpendicular to each other as shown in the figure. Derive an expression for the resultant magnetic field at O.

Knowledge Check

  • A current - carrying loop is shown in the figure. The magnitude of the magnetic field produced at a point O is

    A
    `(mu_(0)I)/(4R)`
    B
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    C
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    D
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